A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands

This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem

Denoising of Natural Images Using the Wavelet Transform

A new denoising algorithm based on the Haar wavelet transform is proposed. The methodology is based on an algorithm initially developed for image compression using the Tetrolet transform. The Tetrolet transform is an adaptive Haar wavelet transform whose support is tetrominoes, that is, shapes made by connecting four equal sized squares. The proposed algorithm improves denoising performance measured in peak signal-to-noise ratio (PSNR) by 1-2.5 dB over the Haar wavelet transform for images corrupted by additive white Gaussian noise (AWGN) assuming universal hard thresholding. The algorithm is local and works independently on each 4x4 block of the image. It performs equally well when compared with other published Haar wavelet transform-based methods (achieves up to 2 dB better PSNR). The local nature of the algorithm and the simplicity of the Haar wavelet transform computations make the proposed algorithm well suited for efficient hardware implementation

An Image Denoising Algorithm Based On Curvelet Transform

Aiming at the limitations of the wavelet transform in image denoising, this paper proposes a new image denoising algorithm based on curvelet transform mathematical method. In this paper, the feasibility of this method is proved by the experimental results. The experiment result shows that, using the proposed new algorithm can get high peak signal to noise ratio, visual effect is very good image

SPECKLE NOISE REDUCTION USING ADAPTIVE MULTISCALE PRODUCTS THRESHOLDING

Image denoising is an essential preprocessing technique in image acquisition systems. For instance, in ultrasound (US) images, suppression of speckle noise while preserving the edges is highly preferred. Thus, in this paper denoising the speckle noise by using wavelet-based multiscale product thresholding approach is presented. The underlying principle of this technique is to apply dyadic wavelet transform and performs the multiscale products of the wavelet transform. Then, an adaptive threshold is calculated and applied to the multiscale products instead of applying it on wavelet coefficient. Thereafter, the performance of the proposed technique is compared with other denoising techniques such as Lee filter, boxcar filter, linear minimum mean square error (LMMSE) filter and median filter. The result shows that the proposed technique gives a better performance in terms of PNSR and ENL value by an average gain of 1.22 and 1.8 times the noisy on, respectively and can better preserved image detail

DENOISING OF HIGH RESOLUTION REMOTE SENSING DATA USING STATIONARY WAVELET TRANSFORM

An image is often corrupted by a noise in its acquisition and transmission. A high resolution remote sensing data will be seen more roughly if it is corrupted by a noise. Wavelet is one of the fascinating denoising manners that will be used to solve this problem. The main application of the Stationary Wavelet Transform (SWT) is denoising. The principle is the average of several denoised signals. Each of them is obtained by using the usual denoising scheme, but it is applied to the coefficients of a ε-decimated DWT. The stationary wavelet transform (SWT) is to make the wavelet decomposition time invariant. This improves the power of wavelet in the signal denoising. In this research, we apply the SWT method to preprocess the remote sensing data for removing the noise. The Worldview-1 satellite data is used in this research. The sensor resolution is 0.55 meters and Ground Sample Distance (GSD) at 20º off-nadir. The Area of Interest (AoI) is Monas, Jakarta and the acquisition of the data was done on March 13th, 2008. For the data analysis, the Worldview-1 satellite data is added by the noise. The result of this research is that the noise can be removed by SWT method. By using structural similarity index (SSIM), the quality of the denoised images by SWT, Wavelet Transform 2D and Wavelet Packet 2D are 0.2666, 0.1912, and 0.1927, respectively. Thus, the SWT provides a better performance in denoising the remote sensing data than Wavelet Packet 2 D and Wavelet 2D methods. Keyword: Denoising, Remote sensing data, Stationary wavelet transfor

Satellite Image Denoising Using Discrete Cosine Transform

The process of adding and removing the noises to an image is said to be as Image denoising. The process can be used in many image applications. This paper presents a method of satellite image denoising scheme using a wavelet transform called as Discrete Cosine Transform (DCT). The noise that is added in this scheme is the salt and pepper noise. By using hard thresholding method in the noise image the co-ordinates of the image can be changed and the original image can be retrieved by removing the noise. This can be done by Inverse Discrete Cosine Transform (IDCT). The performance measures of the proposed system can be done by measuring the PRNR values of the denoised image

Reduced Cycle Spinning Method for the Undecimated Wavelet Transform

[EN] The Undecimated Wavelet Transform is commonly used for signal processing due to its advantages over other wavelet techniques, but it is limited for some applications because of its computational cost. One of the methods utilized for the implementation of the Undecimated Wavelet Transform is the one known as Cycle Spinning. This paper introduces an alternative Cycle Spinning implementation method that divides the computational cost by a factor close to 2. This work develops the mathematical background of the proposed method, shows the block diagrams for its implementation and validates the method by applying it to the denoising of ultrasonic signals. The evaluation of the denoising results shows that the new method produces similar denoising qualities than other Cycle Spinning implementations, with a reduced computational cost.This research was funded by grants number PGC2018-09415-B-I00 (MCIU/AEI/FEDER, UE) and TEC2015-71932-REDT.Rodríguez-Hernández, MA. (2019). 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Color Extension of Monogenic Wavelets with Geometric Algebra : Application to Color Image Denoising

10 pagesInternational audienceWe define a color monogenic wavelet transform. This is based on the recent grayscale monogenic wavelet transform and an extension to color signals aimed at defining non-marginal tools. Wavelet based color image processing schemes have mostly been made by using a grayscale tool separately on color channels. This may have some unexpected effect on colors because those marginal schemes are not necessarily justified. Here we propose a definition that considers a color (vector) image right at the beginning of the mathematical definition so we can expect to bring an actual color wavelet transform - which has not been done so far to our knowledge. This so provides a promising multiresolution color geometric analysis of images. We show an application of this transform with a statistical modeling of coefficients for color denoising issue